About the Hardy Inequality

2011 ◽  
pp. 165-180 ◽  
Author(s):  
Nader Masmoudi
Keyword(s):  
Hardy Inequality ◽  
The Hardy Inequality

scholarly journals Hardy-type inequalities for Dunkl operators with applications to many-particle Hardy inequalities

2020 ◽  
pp. 2050024 ◽  
Author(s):  
Andrei Velicu
Keyword(s):  
Hardy Inequality ◽  
Root Systems ◽  
Dunkl Operators ◽  
Hardy Inequalities ◽  
One Dimensional ◽  
Hardy Type Inequalities ◽  
Rellich Inequality ◽  
Nirenberg Inequality ◽  
Special Case ◽  
The Hardy Inequality

In this paper, we study various forms of the Hardy inequality for Dunkl operators, including the classical inequality, [Formula: see text] inequalities, an improved Hardy inequality, as well as the Rellich inequality and a special case of the Caffarelli–Kohn–Nirenberg inequality. As a consequence, one-dimensional many-particle Hardy inequalities for generalized root systems are proved, which in the particular case of root systems [Formula: see text] improve some well-known results.

scholarly journals The Prehistory of the Hardy Inequality

2006 ◽  
Vol 113 (8) ◽  
pp. 715 ◽  
Author(s):  
Alois Kufner ◽  
Lech Maligranda ◽  
Lars-Erik Persson
Keyword(s):  
Hardy Inequality ◽  
The Hardy Inequality

scholarly journals INEQUALITIES ASSOCIATED WITH DILATIONS

2009 ◽  
Vol 11 (02) ◽  
pp. 265-277 ◽  
Author(s):  
TOHRU OZAWA ◽  
HIRONOBU SASAKI
Keyword(s):  
Hardy Inequality ◽  
Sobolev Type ◽  
Semi Group ◽  
The Hardy Inequality

Some properties of distributions f satisfying x · ∇ f ∈ Lp (ℝn), 1 ≤ p < ∞, are studied. The operator x · ∇ is the generator of a semi-group of dilations. We first give Sobolev type inequalities with respect to the operator x · ∇. Using the inequalities, we also show that if [Formula: see text], x · ∇ f ∈ Lp (ℝn) and |x|n/p|f(x)| vanishes at infinity, then f belongs to Lp (ℝn). One of the Sobolev type inequalities is shown to be equivalent to the Hardy inequality in L2 (ℝn).

The Hardy Inequality for Hermite Expansions

2014 ◽  
Vol 21 (2) ◽  
pp. 267-280 ◽  
Author(s):  
Zhongkai Li ◽  
Yufeng Yu ◽  
Yehao Shi
Keyword(s):  
Hardy Inequality ◽  
Hermite Expansions ◽  
The Hardy Inequality

Hardy’s inequality on Hardy–Morrey spaces

2019 ◽  
Vol 26 (3) ◽  
pp. 405-413 ◽  
Author(s):  
Kwok-Pun Ho
Keyword(s):  
Hardy Inequality ◽  
Morrey Spaces ◽  
Hardy’S Inequality ◽  
Hardy's Inequality ◽  
The Hardy Inequality

Abstract We generalize the Hardy inequality to Hardy–Morrey spaces.

scholarly journals A stronger extension of the hardy inequality

1998 ◽  
Vol 270 (1-3) ◽  
pp. 275-286 ◽  
Author(s):  
Lie-heng Wang ◽  
Ya-xiang Yuan
Keyword(s):  
Hardy Inequality ◽  
The Hardy Inequality

On the Hardy inequality with measures

2008 ◽  
Vol 78 (3) ◽  
pp. 843-845
Author(s):  
D. V. Prokhorov
Keyword(s):  
Hardy Inequality ◽  
The Hardy Inequality
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